The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.
To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.
Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.
To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:
P(x) = x(24 - x)
This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.
The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.
To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.
Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.
So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.
Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.
To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]
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HELPPPP!!!!!!!!
(04.04 MC)
As shoppers left a supermarket, they were asked if they used a shopping list and if they bought more items than they expected. The table contains the results.
Bought only the expected items Bought more items than expected Row Totals
Had a shopping list 0.43 0.17 0.60
Did not have a shopping list 0.22 0.18 0.40
Column Totals 0.65 0.35 1.00
If a customer purchased more items than planned, what is the likelihood that the customer did not use a shopping list? Round your answer to two decimal places.
0.51
0.49
0.28
0.17
The likelihood that a customer who purchased more items than planned did not use a shopping list is approximately 0.51.
To determine the likelihood that a customer who purchased more items than planned did not use a shopping list, we need to calculate the conditional probability.
Let's focus on the "Bought more items than expected" column. The probability that a customer did not use a shopping list is given by the ratio of the "Did not have a shopping list" value in that column to the total value in that column.
The probability that a customer did not use a shopping list given that they bought more items than expected is:
0.18 / 0.35 ≈ 0.51 (rounded to two decimal places)
Consequently, the probability that a consumer who spent more money than anticipated did not make a shopping list is roughly 0.51.
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Given the husband
has between $100,000
and $150,000
of insurance, what is the probability that the wife
has more than $150,000
of insurance? Round your final answer to four decimal places. Do not round intermediate answers.
The probability that the wife has more than $150,000 in insurance is given as follows:
0.2446 = 24.46%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.The number of outcomes in which the husband has a insurance in the desired range is given as follows:
50 + 30 + 25 + 34 = 139.
The number of outcomes in which both have insurance in the desired range is given as follows:
34.
Hence the probability is given as follows:
34/139 = 0.2446.
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please answer fast...............................
The coordinate of point R after the rotation is determined as = ( - 4, 7).
option A.
What is the rotation of a figure?A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.
When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.
The initial coordinate of point R = ( 4, 7),
The new coordinate of point R after the rotation = ( - 4, 7)
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Suppose we lined up all the people in the world (about 7.4 billion people). Assume that each person occupied 12 inches of the line. How many times around Earth would they reach? (Earth has a circumference of about 25,000 miles. Round your answer to one decimal place.)
If we lined up all the people in the world (about 7.4 billion people) and assume that each person occupied 12 inches of the line, the number of times around Earth that they would reach would be: 59.1 times
How to determine the number of timesTo determine the number of times that all the people on the earth will move around the planet the dimensions above would be gotten by first harmonizing the dimensions.
1 mile = 63360 inches
So, 25,000 miles = 1.58 * 10⁹ in
Now we multiply the number of people on the earth and divide this number u the circumference in inches.
7.4 * 10⁹ * 12
= 88.8 * 10⁹
88.8 * 10⁹/1.58 * 10⁹ in
= 59.1
So all the people on the earth will move around its circumference, 59.1 times.
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Need help with this pls help!!!!
The five-number summary for the height of 18 sunflowers include:
Minimum (Min) = 40.First quartile (Q₁) = 50.Median (Med) = 55.Third quartile (Q₃) = 55.75.Maximum (Max) = 63.How to determine the five-number summary for the data?In order to determine the five-number summary for the height of 18 sunflowers, we would arrange the data set in an ascending order:
40, 45, 47, 50, 50, 51, 51, 51, 55, 55, 55, 55, 55, 55, 58, 58, 62, 63
From the data set above, we can logically deduce that the minimum (Min) is equal to 40.
For the first quartile (Q₁), we have:
Q₁ = [(n + 1)/4]th term
Q₁ = (18 + 1)/4
Q₁ = 4.75th term
Q₁ = 4th term + 0.75(5th term - 4th term)
Q₁ = 50 + 0.75(50 - 50)
Q₁ = 50 + 0.75(0)
Q₁ = 50.
From the data set above, we can logically deduce that the median (Med) is given by:
Median = (9th term + 10th term)/2
Median = (55 + 55)/2
Median = 55
For the third quartile (Q₃), we have:
Q₃ = [3(n + 1)/4]th term
Q₃ = 3 × 4.75
Q₃ = 14.25th term
Q₃ = 14th term + 0.25(15th term - 14th term)
Q₃ = 55 + 0.25(58 - 55)
Q₃ = 55 + 0.25(3)
Q₃ = 55.75
In conclusion, the maximum height is equal to 63.
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if the standard deviation of 3,6,x,7,5 is square root 2 find the positive value of x
Using the formula for the standard deviation and solving for x, we will get:
x = 7.6
How to find the value of x?To find the positive value of 'x' in the given set of numbers (3, 6, x, 7, 5) when the standard deviation is √2, we can use the formula for standard deviation.
The formula for calculating the sample standard deviation is as follows:
σ = √[(Σ(xi - m)²) / (n - 1)]
Where:
σ is the standard deviationΣ is the summation symbolxi represents each value in the datasetm is the mean of the datasetn is the number of values in the datasetFirst, let's calculate the mean (m) of the given set of numbers:
Mean (m) = (3 + 6 + x + 7 + 5) / 5 = (21 + x) / 5
Next, let's substitute the values into the standard deviation formula:
√2 = √[( (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)² ) / 4]
Simplifying the equation:
2 = [( (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)² ) / 4]
Multiplying both sides of the equation by 4:
8 = (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)²
Expanding and simplifying:
8 = (15 - (21 + x) / 5)² + (30 - (21 + x) / 5)² + (5x/5)² + (35 - (21 + x) / 5)² + (25 - (21 + x) / 5)²
8 = (15 - (21 + x) / 5)² + (30 - (21 + x) / 5)² + x² + (35 - (21 + x) / 5)² + (25 - (21 + x) / 5)²
Expanding and simplifying further:
8 = (225 - 2(21 + x) + (21 + x)² / 25) + (900 - 2(21 + x) + (21 + x)² / 25) + x² + (1225 - 2(21 + x) + (21 + x)² / 25) + (625 - 2(21 + x) + (21 + x)² / 25)
Combining like terms:
8 = (225 + 900 + 1225 + 625) / 25 - 10(21 + x) + 5(21 + x)² / 25 + x²
8 = 2975 / 25 - 10(21 + x) + 5(21 + x)² / 25 + x²
Simplifying:
8 = 119 - 10(21 + x) + (21 + x)² / 5 + x²
Rearranging the terms:
8 - 119 = -10(21 + x) + (21 + x)² / 5 + x²
-111 = -10(21 + x) + (21 + x)² / 5 + x²
Multiplying through by 5 to eliminate the fraction:
-555 = -50(21 + x) + (21 + x)² + 5x²
Expanding and simplifying:
-555 = -1050 - 50x + x² + 441 + 42x + x² + 5x²
Combining like terms:
0 = 7x² - 8x - 114
Now, we can solve this quadratic equation to find the value of 'x'.
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 7, b = -8, and c = -114.
Plugging the values into the formula:
x = (-(-8) ± √((-8)² - 4(7)(-114))) / (2(7))
Simplifying:
x = (8 ± √(64 + 3192)) / 14
x = (8 ± 2√(814)) / 14
x = (4 ± √(814)) / 7
Therefore, the values of 'x' that satisfy the given equation are approximately:
x ≈ (4 + √(814)) / 7 ≈ 7.62
x ≈ (4 - √(814)) / 7 ≈ -0.29
Since we are looking for the positive value of 'x', the solution is:
x ≈ 7.6
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To solve a(b + c) = d for a in 1 step:
Answer:
a = [tex]\frac{d}{b+c}[/tex]
Step-by-step explanation:
a(b + c) = d
isolate a by dividing both sides by b + c
a = [tex]\frac{d}{b+c}[/tex]
calculating area of cylinder pls help x
How to solve this question?l
The proportional relationship that models the data in the table is given as follows:
y = 0.7x.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The constant for this problem is given as follows:
k = 7/10 = 14/20 = 21/30 = 0.7.
(constant is obtained dividing the output by it's respective input).
Hence the equation is given as follows:
y = 0.7x.
Missing InformationThe problem asks for the proportional relationship that defines the data in the table.
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Carys is checking a tax bill for the last year
Carys is reviewing her tax bill for the previous year to ensure accuracy and compliance with tax regulations.
Carys checking a tax bill for the last year involves reviewing and verifying the information related to her tax obligations and payments for that specific year. This process typically includes several steps:
Gathering relevant documents: Carys would collect all the necessary documents, such as income statements (W-2 or 1099 forms), expense receipts, investment statements, and any other relevant financial documents.
Reviewing income sources: Carys would examine all the sources of income she received during the year, including employment income, self-employment income, rental income, investment income, etc. She would ensure that all income sources are accurately reported and accounted for.
Deductions and credits: Carys would assess if she is eligible for any deductions or tax credits that can reduce her taxable income or provide tax benefits. These may include deductions for expenses like mortgage interest, medical expenses, education expenses, and credits such as the Child Tax Credit or the Earned Income Tax Credit.
Calculating taxable income: Carys would determine her taxable income by subtracting eligible deductions and adjustments from her total income. This step helps in determining the portion of income that is subject to taxation.
Applying tax rates: Carys would review the applicable tax brackets and rates to calculate her income tax liability based on her taxable income. Different income levels are subject to different tax rates, and Carys would ensure she is applying the correct rates.
Checking for errors: Carys would carefully review all calculations and entries on her tax return to identify any errors or discrepancies. This includes verifying that all income, deductions, and credits are accurately reported and that the final tax liability is correctly calculated.
Filing the tax return: Once Carys is satisfied with the accuracy of her tax bill, she would file her tax return with the appropriate tax authority, such as the Internal Revenue Service (IRS) in the United States. This step involves submitting the required forms and supporting documents to report her income and claim any applicable deductions or credits.
By going through these steps, Carys can ensure that her tax bill for the last year is accurate, complete, and in compliance with the tax regulations and laws of her jurisdiction.
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What is the simplified form of the following expression?
5√8-√18-2√2
O2-√2
O 5√2
O9-√2
O15-√2
Answer:
9 square root 2 is correct answer
Please look at the photo.
Finding the absolute maximum and minimum of a function.
Please answer all 4 parts of the question.
a. The absolute maximum of g is 2.
The absolute minimum of g is -4.
b. The absolute maximum of h is 1.
The absolute minimum of h is -3.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 2 while the absolute minimum of g is -4.
In conclusion, the absolute maximum of the polynomial function h is 1 while the absolute minimum of h is -3.
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Saylin received $325 in gifts for her 8th Grade Moving Up Ceremony. She plans on investing all of it in an account earning 4.25% interest compounded annually. How much money will be in the account in four years?
A) $877.50
B) $383.87
C) $1340.12
D) $138.13
To calculate the future value of the investment, we can use the formula for compound interest:
[tex]\sf A = P \left(1 + \frac{r}{n}\right)^{nt}[/tex]
where:
[tex]\sf A[/tex] = the future value of the investment
[tex]\sf P[/tex] = the initial principal (amount invested)
[tex]\sf r[/tex] = the interest rate (as a decimal)
[tex]\sf n[/tex] = the number of times interest is compounded per year
[tex]\sf t[/tex] = the number of years
In this case, Saylin received $325 and plans to invest it for 4 years at an interest rate of 4.25% compounded annually.
Substituting the values into the formula, we have:
[tex]\sf A = 325 \left(1 + \frac{0.0425}{1}\right)^{(1 \times 4)}[/tex]
Simplifying the equation:
[tex]\sf A = 325 \times 1.0425^4[/tex]
Calculating the expression, we find:
[tex]\sf A \approx 383.87[/tex]
Therefore, the amount of money in the account after 4 years will be approximately $383.87. Thus, the correct option is B) 383.87.
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How to solve this question?
The proportional relationship that models the data in the table for this problem is given as follows:
y = 0.7x.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The constant for this problem is given as follows:
k = 7/10 = 14/20 = 21/30 = 0.7.
Hence the equation is given as follows:
y = 0.7x.
Missing InformationThe problem asks for the proportional relationship that defines the data in the table.
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A project on Kickstarter for an iPad stylus raised 1,372% of their goal, raising a total of $318,544 from 7,529 supporters. What was their original goal?
The original goal of the Kickstarter project was $23,217.49.
Here's the calculation:
Original goal = $318,544 / (1372% / 100)
= $318,544 / 1.372
= $23,217.49
The project was able to raise more than 13 times its original goal, which is a great success. It shows that there is a high demand for the product and that the project team was able to effectively market it to potential backers.
3) Find x, y, and z.
x = ___
y = ___
z = ___
Answer:
z= 118
y= 118
x= 62
Step-by-step explanation:
When parallel lines have two transversal lines, a set of corresponding angles, alternate angles, interior angles, and vertical angles are formed.
Corresponding angles are found on the same parallel line but are formed by different transversal lines and are equal. An example of this is the angle marked as 118 and z. therefore z=118
Vertical angles are angles found Infront of each other, they are equal. An example of vertical angles are angle y and angle z. Therefore angle y = angle z. y= 118
angle y also corresponds to point C. point C is 180 -x. Therefore x= 180-118 which is 62. x=62
A number cube with faces labeled 1 to 6 is rolled once. The number rolled will be recorded as the outcome. Consider the following events. Event A: The number rolled is even. Event B: The number rolled is less than 4.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event B:
The answers are given below:
a) A ∪ B = {1, 2, 3, 4, 6}
b) A ∩ B = {2}
c) Bc = {1, 3, 5}
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that a number cube with faces labelled 1 to 6 is rolled once. The number rolled will be recorded as the outcome.
A number cube with faces labelled 1 to 6.
Therefore the set of all possible outcomes is {1, 2, 3, 4, 5, 6}.
Event A
The number rolled is even.
Therefore, the set of outcomes for event A is {2, 4, 6}.
Event B
The number rolled is less than 4.
Therefore, the set of outcomes for event B is {1, 2, 3}.
Part (a)
Event "A or B" means the outcomes in A or B or both.
[tex]\Rightarrow \text{A} \cup \text{B} = \{1,2,3,4,6\}[/tex]
Part (b)
Event "A and B" means the outcomes in both A and B.
[tex]\Rightarrow \text{A} \cap \text{B} = \{2\}[/tex]
Part (c)
The complement of event B means everything that is not in B.
[tex]\Rightarrow \text{B}\text{c} = \{1,3,5\}[/tex]
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A man walks up 800m road AB which slopes at 10.2 to the horizon. He then walks 300m down road BC, which is at 6.3 to the horizon. The horizon is parallel to AD and BF perpendicular to AD. Find the length of CD
The length of CD is approximately 27.931 meters.
To find the length of CD, we can use the concept of similar triangles and trigonometric ratios.
Let's start by drawing a diagram to visualize the situation:
A----------B
/ /
/ /
/ /
D----------C
|
|
|
F
We are given that road AB slopes at 10.2 degrees to the horizon and road BC slopes at 6.3 degrees to the horizon. From the diagram, we can see that angle DAF is the same as the slope angle of road AB (10.2 degrees), and angle DCF is the same as the slope angle of road BC (6.3 degrees).
Now, we can set up the following trigonometric equations using the given information:
tan(10.2 degrees) = CD / AD (equation 1)
tan(6.3 degrees) = CD / BF (equation 2)
Since AD and BF are perpendicular, we can consider them as vertical heights. Let's calculate the lengths of AD and BF.
For road AB, we can use the definition of tangent:
tan(10.2 degrees) = height AB / length AB
Solving for the height AB, we have:
height AB = tan(10.2 degrees) * length AB
height AB = tan(10.2 degrees) * 800m
height AB ≈ 147.294m
Similarly, for road BC:
height BC = tan(6.3 degrees) * length BC
height BC = tan(6.3 degrees) * 300m
height BC ≈ 33.706m
Now, we can substitute these values into equations 1 and 2:
tan(10.2 degrees) = CD / 147.294m (equation 1)
tan(6.3 degrees) = CD / 33.706m (equation 2)
Solving equation 1 for CD:
CD = tan(10.2 degrees) * 147.294m
CD ≈ 27.931m
Therefore, the length of CD is approximately 27.931 meters.
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The population of a town increased from 3700 in 2005 to 5900 in 2009. Find the absolute and relative (percent) increase.
Absolute increase:
Relative increase:
%
The absolute increase in population is 2200, and the relative increase is approximately 59.46%.
To find the absolute and relative increase in population, we can use the following formulas:
Absolute increase = Final value - Initial value
Relative increase = (Absolute increase / Initial value) * 100%
Given the population in 2005 is 3700 and the population in 2009 is 5900, we can calculate the absolute and relative increase as follows:
Absolute increase = 5900 - 3700 = 2200
To calculate the relative increase, we need to divide the absolute increase by the initial value and then multiply by 100:
Relative increase = (2200 / 3700) * 100% ≈ 59.46%
Therefore, the absolute increase in population is 2200, and the relative increase is approximately 59.46%.
The absolute increase represents the actual difference in population count between the two years, while the relative increase gives us the percentage change relative to the initial value. In this case, the population increased by 2200 individuals, and the relative increase indicates that the population grew by approximately 59.46% over the given period.
Note that the relative increase is expressed as a percentage, which makes it easier to compare changes across different populations or time periods.
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Question 4 A ladder 12 m long leans against a vertical wall with its foot 4.5 m away from the base of the wall as shown. What height does the ladder reach up the wall? (Leave your answer in 2 decimal places).
To find the height that the ladder reaches up the wall, we can use the Pythagorean theorem.
which relates the lengths of the sides of a right triangle. In this case, the ladder forms the hypotenuse, the distance from the base of the wall to the foot of the ladder is one side (4.5 m), and the height we want to find is the other side.
In this case, the ladder forms the hypotenuse, and the distance from the foot of the ladder to the base of the wall is one of the sides.
Let's denote the height of the ladder on the wall as 'h'. According to the problem, the length of the ladder is 12 m, and the distance from the foot of the ladder to the base of the wall is 4.5 m.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where a represents the height, b represents the distance from the base of the wall, and c represents the length of the ladder.
Substituting the given values, we have:
a^2 + (4.5)^2 = (12)^2
Simplifying:
a^2 + 20.25 = 144
a^2 = 144 - 20.25
a^2 = 123.75
Taking the square root of both sides:
a ≈ 11.11
Therefore, the ladder reaches a height of approximately 11.11 meters up the wall.
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[tex] \sf{\blue{«} \: \pink{ \large{ \underline{Q\orange{U} \red{E} \green{S} \purple{TI} \pink{{ON}}}}}}[/tex]
In ∆ABC, D and E are the points on the sides AB and AC respectively such that DE || BC. If AD = 6x – 7, DB = 4x – 3, AE = 3x – 3, and EC = 2x – 1 then find. the value of ‘x’.
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[tex] \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}[/tex]
To find the value of 'x', we can use the property of parallel lines that states when a transversal intersects two parallel lines, the corresponding angles are equal.
In triangle ABC, we have DE parallel to BC. Therefore, we can conclude that triangle ADE is similar to triangle ABC.
Using the property of similar triangles, we can set up the following proportion:
[tex]\displaystyle\sf \dfrac{AD}{DB} = \dfrac{AE}{EC}[/tex]
Substituting the given values:
[tex]\displaystyle\sf \dfrac{6x - 7}{4x - 3} = \dfrac{3x - 3}{2x - 1}[/tex]
To solve this proportion for 'x', we can cross-multiply:
[tex]\displaystyle\sf (6x - 7)(2x - 1) = (4x - 3)(3x - 3)[/tex]
Expanding both sides:
[tex]\displaystyle\sf 12x^{2} - 6x - 14x + 7 = 12x^{2} - 9x - 12x + 9[/tex]
Combining like terms:
[tex]\displaystyle\sf 12x^{2} - 20x + 7 = 12x^{2} - 21x + 9[/tex]
Moving all terms to one side:
[tex]\displaystyle\sf 12x^{2} - 12x^{2} - 20x + 21x = 9 - 7[/tex]
Simplifying:
[tex]\displaystyle\sf x = 2[/tex]
Therefore, the value of 'x' is 2.
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Answer:
Step-by-step explanation:
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.
It is given that AD=4x−38, BD=3x−1, AE=8x−7 and CE=5x−3. Let AC=x
Using the basic proportionality theorem, we have
BD
AD
=
AC
AE
⇒
3x−1
4x−3
=
x
8x−5
⇒x(4x−3)=(3x−1)(8x−5)
⇒4x
2
−3x=3x(8x−5)−1(8x−5)
⇒4x
2
−3x=24x
2
−15x−8x+5
⇒4x
2
−3x=24x
2
−23x+5
⇒24x
2
−23x+5−4x
2
+3x=0
⇒20x
2
−20x+5=0
⇒5(4x
2
−4x+1)=0
⇒4x
2
−4x+1=0
⇒(2x)
2
−(2×2x×1)x+1
2
=0(∵(a−b)
2
=a
2
+b
2
−2ab)
⇒(2x−1)
2
=0
⇒(2x−1)=0
⇒2x=1
⇒x=
2
1
Hence, x=
2
1
.
Please help me with this question, too.
The value of the result of the expression from the computation is [tex]7.54 * 10^-1[/tex]
What is standard form?Standard form refers to a specific format or notation used to represent mathematical equations or numbers.
When referring to the standard form of a number, it usually means expressing a number in scientific notation or standard index form. In scientific notation, a number is written as a product of a decimal number between 1 and 10 and a power of 10.
We can write the given problem as;
[tex]3.77 * 10^-7 * 1.4 * 10^3/7 * 10^4\\= 7.54 * 10^-1[/tex]
This is the required format.
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Using the Pythagorean Theorem, prove whether or not the following triangle is a right
triangle. Remember to show your work.
A triangle with side lengths of 13m, 5m and 10m
A) Is it a right triangle (1 point)
B) Explain and show your work (4 points)
A) The triangle is not a right triangle.
B) Based on the calculations, the square of the longest side is not equal to the sum of the squares of the other two sides, indicating that the triangle does not meet the criteria of a right triangle according to the Pythagorean Theorem.
To determine if the triangle with side lengths 13m, 5m, and 10m is a right triangle, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate the squares of the side lengths:
13^2 = 169
5^2 = 25
10^2 = 100
According to the Pythagorean Theorem, if this triangle is a right triangle, the square of the longest side (13^2 = 169) should be equal to the sum of the squares of the other two sides (5^2 + 10^2 = 25 + 100 = 125).
Since 169 is not equal to 125, we can conclude that the triangle with side lengths 13m, 5m, and 10m is not a right triangle. The sum of the squares of the shorter sides is less than the square of the longest side, which does not satisfy the condition for a right triangle.
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Find an equation of a line in a point-slope form passing through the points (2,4) and (3,6) . Then write the answer in a slope-intercept form. Then write the answer in standard form. Graph the line on cartesian plane and upload the image. Show your work (the steps)!
The equation of the line in point-slope form, slope-intercept form and standard form is y - 4 = 2( x - 2 ), y = 2x and 2x - y = 0 respectively.
What is the equation of line passing through the points (2,4) and (3,6)?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given that the line passes through points (2,4) and (3,6).
First, we determine the slope:
[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 4}{3-2} \\\\Slope\ m = \frac{2}{1} \\\\Slope\ m = 2[/tex]
Now, plug the slope m = 2 and point (2,4) into the point-slope form:
( y - y₁ ) = m( x - x₁ )
y - 4 = 2( x - 2 )
Solve in slope-intercept form:
y - 4 = 2( x - 2 )
y - 4 = 2x - 4
y = 2x - 4 + 4
y = 2x
Solve in standard form:
Ax + Bx = C
y - y = 2x - y
0 = 2x - y
Reorder:
2x - y = 0
Therefore, the standard form is 2x - y = 0.
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Prove segment EG is congruent to segment HF.
Both EG and HF are expressed in terms of x and their Coefficients are equal (9 and 7), we can conclude that EG is congruent to HF. This means that segment EG and segment HF have the same length.
To prove that segment EG is congruent to segment HF, we need to show that they have the same length.
Given the information provided, we can use the fact that points E, F, G, and H lie on the same line segment in that order. Let's assume that the distances from E to F, F to G, and G to H are denoted as EF, FG, and GH, respectively.
According to the given information, the ratio of EF to FG to GH is equal to 4/5/2. This implies that EF is 4 parts, FG is 5 parts, and GH is 2 parts of the total length of the line segment.
Let's denote the length of EG as x. Since EG is the combination of EF and FG, we can express it as EF + FG. From the given information, EF is 4 parts and FG is 5 parts. Therefore, we can write:
EG = EF + FG = 4x + 5x = 9x.
Similarly, we can denote the length of HF as y. Since HF is the combination of FG and GH, we can express it as FG + GH. From the given information, FG is 5 parts and GH is 2 parts. Therefore, we can write:
HF = FG + GH = 5x + 2x = 7x.
Now, we have expressed the lengths of EG and HF in terms of x. To prove that EG is congruent to HF, we need to show that they have the same length. This can be done by comparing their expressions:
EG = 9x
HF = 7x
Since both EG and HF are expressed in terms of x and their coefficients are equal (9 and 7), we can conclude that EG is congruent to HF. This means that segment EG and segment HF have the same length.
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CALCULA EL VOLÚMEN DE LOS SIGUIENTES PRISMAS.
PRISMA RECTANGULAR: BASE 8 CM, ALTURA 12CM, Y ALTURA DEL CUERPO 35CM.
con procedimiento
El volumen del prisma 3360 cm³
Que es una ecuacion?Una ecuación es una expresión que muestra la relación entre dos o más números y variables.
El volumen de un prisma viene dado por:
volumen = largo * ancho * alto
De la pregunta:
Largo = 35 cm, ancho = 8 cm y alto = 12 cm, por lo tanto:
Volumen = 35 * 12 * 8 = 3360 cm³
El volumen es 3360 cm³
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Two buildings are 18 m part. The shorter building is 12 m high while the taller one is 19 m high. Find the distance, x m between the top of the buildings.
The distance between the tops of the buildings is 28.5 meters.
To find the distance between the top of the buildings, we can use the concept of similar triangles.
Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).
We can set up a proportion based on the similar triangles formed by the buildings:
a/c = b/x
Substituting the known values:
12/18 = 19/x
To find "x," we can cross-multiply and solve for "x":
12x = 18 * 19
12x = 342
x = 342/12
x = 28.5 m
Therefore, the distance between the tops of the buildings is 28.5 meters.
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Realiza la gráfica de una Elipse y determina los elementos que la componen (8 elementos).
2.- Los vértices de una elipse son los puntos V1 (-1, -8) y V2 (11, -8) y la longitud de cada lado recto es 6/2. Hallar la ecuación de la Elipse, el valor de su excentricidad y realiza su gráfica.
3.- Una Elipse tiene un eje mayor que coincide con el eje de las
Ordenadas (Y), los focos están ubicados en F1 (0, 3) y F2 (0, -3), y el valor de la excentricidad es de ½. Encontrar;
a) La ecuación de la Elipse
b) La longitud del eje Mayor
c) La longitud del eje Menor
d) La longitud de cada Lado Recto
e) Gráfica de la Elipse
4.- Realiza la Gráfica de una Hipérbola y determina los elementos que la componen (8 elementos).
The elements that compose an ellipse are:
1. Center: The center is the point in the middle of the ellipse. It is denoted as (h, k), where h represents the x-coordinate and k represents the y-coordinate of the center.
2. Major Axis: The major axis is the longer of the two axes of the ellipse. It passes through the center and is perpendicular to the minor axis.
3. Minor Axis: The minor axis is the shorter of the two axes of the ellipse. It also passes through the center and is perpendicular to the major axis.
4. Vertices: The vertices are the points on the ellipse where the major axis intersects the ellipse. In this case, the vertices are V1(-1, -8) and V2(11, -8).
5. Co-vertices: The co-vertices are the points on the ellipse where the minor axis intersects the ellipse.
6. Foci: The foci are two points inside the ellipse that help define its shape. The sum of the distances from any point on the ellipse to the two foci is constant. In the given problem, the foci are F1(0, 3) and F2(0, -3).
7. Eccentricity: The eccentricity of an ellipse is a measure of how "squished" or elongated the ellipse is. It is denoted by the letter e and is calculated by dividing the distance between the center and one of the foci by the distance between the center and a vertex.
To find the equation of the ellipse, you can use the standard form equation:
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Where (h, k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes respectively.
To find the length of the major axis, you can simply double the length of the semi-major axis.
To find the length of the minor axis, you can double the length of the semi-minor axis.
To find the length of each side of the rectangle, you can use the formula 2 * b.
To graph the ellipse, plot the center, vertices, co-vertices, and foci on a coordinate plane and sketch the shape of the ellipse using these points.
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10. Higher Order Thinking Each of 5 friends has x action figures in
his or her collection. Each friend buys 11 more action figures. Now
the 5 friends have a total of 120 action figures.
a. Write an equation that models the problem.
b. Solve the equation to find the number of action figures, x, that
each friend had originally.
Each friend had originally 13 action figures before buying 11 more.
Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.
a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.
Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.
The total number of action figures will be 5(x + 11) = 5x + 55.
Now, according to the problem,5x + 55 = 120
This is our equation that models the problem.
b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.
5x + 55 = 120
5x = 120 - 55 (subtract 55 from both sides)
5x = 65x = 13
Therefore, each friend had originally 13 action figures before buying 11 more.
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Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent (E), above average (AA), average (A), below average (BA), or poor (P). The ratings provided by a sample of 20 guests are shown below. Give the frequencies, in order, for the frequency distribution shown.
Question 1 options:
1, 7, 7, 3, 2
1, 8, 6, 3, 2
2, 7, 6, 3, 2
1, 2, 3, 6, 5
The frequencies, in order, for the frequency distribution shown are 1, 7, 7, 3, 2.
The correct answer is: 1, 7, 7, 3, 2
To determine the frequencies for the given ratings, let's analyze the data provided:
Excellent (E): 1
Above Average (AA): 7
Average (A): 7
Below Average (BA): 3
Poor (P): 2
To find the frequencies, we count the number of occurrences for each rating:
Frequency of Excellent (E): 1
Frequency of Above Average (AA): 7
Frequency of Average (A): 7
Frequency of Below Average (BA): 3
Frequency of Poor (P): 2
Now, let's list the frequencies in order:
1, 7, 7, 3, 2.
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